Legal aid will only pay for custody and child support, it won't cover costs for anything else. Very few lawyers accept legal aid certificates, although if you get a lawyer that has experience with a lot of clients with low income then they will be able to understand your needs better as well as the barriers you have to overcome to get your life back on track.
The Child Support Tables don't apply to incomes over about 150k, and your wife earns 340k so the tables are out the window. The CS will be determined according to your individual case, not a formula. Probably this is to your favour.
You definately qualify for spousal support, and you should try to get some retraining or a degree for yourself to move on in life. This isn't just financial, it will help your self esteem and help you rebuild your social life and give you some direction. It makes a huge difference to your emotional state to see a new beginning ahead instead of focusing on the crap that is behind you.
Your lawyer can argue that spousal support to enable you to retrain is in your ex's best interest as well as the best interest of the kids. Getting you on your feet takes the pressure off of her and sets a great example for your children.
I am in a similar position to you, my ex wife makes 5x my income, and I spent years working part time and caring for the kids after school. Society, culture, family expectations, parents, etc, all put a huge pressure on men to conform to the breadwinner, and it will really hit you hard at times. Remember that this is your right, it is a right hard fought for, and your support of your wife is what allowed her to focus on her career. That career was an investment the two of you made together.
Good luck.